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Measuring the strangeness of strange attractors

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book 01 Oct 1983Publisher:Elsevier BVJournal:Physica D: Nonlinear Phenomena, volume 9, pages 189-208 (issn: 0167-2789,

Authors: Itamar Procaccia; Peter Grassberger; Peter Grassberger;

doi: 10.1016/0167-2789(83)90298-1 , 10.1007/978-0-387-21830-4_12

Measuring the strangeness of strange attractors

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Abstract

The authors consider the question of which observables may be effectively used to distinguish chaos and random noise in a dynamical system possessing a strange attractor. After briefly reviewing some such quantities (fractal dimension, Lyapunov exponents information entropy), the authors suggest another such measure, the correlation exponent. This exponent is closely related to the above quantities, but its computation is considerably easier. The authors then describe this exponent in a variety of examples.

Related Organizations

Weizmann Institute of Science
Israel
University of Wuppertal
Germany

Keywords

random noise, fractal dimension, chaos, Lyapunov exponents, information entropy, strange attractor, Strange attractors, chaotic dynamics of systems with hyperbolic behavior, correlation exponent, Fractals, Entropy and other invariants, isomorphism, classification in ergodic theory, Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)

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	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	5K
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	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 0.01%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%